Explore Reasons Behind Dramatic Difference between AQI’s by U.S. and Chinese government
author: Li Luo, Zhuangye Chen date: 02/10/2016 font-family: ‘Helvetica’
Overview
- Background
- Adjustment Based On Breakpoints
- Dates with 10 Biggest AQI Difference
- Stationary Test
- Seasonal Trend Decomposition
Background
How is Air Quality Index (AQI) calculated?
- For the pollutant \(p\), define IAQI (Individual AQI) as:
\[
IAQI_p = \frac{I_{high} - I_{low}}{C_{high} - C_{low}} (C - C_{low}) + I_{low}
\] \(C\) = the pollutant concentration
\(C_{low}\)= the concentration breakpoint that is \(\le C\)
\(C_{high}\)= the concentration breakpoint that is \(\ge C\)
\(I_{low}\)= the index breakpoint corresponding to \(C_{low}\)
\(I_{high}\)= the index breakpoint corresponding to \(C_{high}\)
- \[AQI = max\{ IAQI_1, IAQI_2, IAQI_3,\dots, IAQI_n\}\]
Different Breakpoints
| PM2.5 (\(\mu g/m^3\)) | AQI by China | AQI by U.S. |
|---|---|---|
| 0 | 0 | 0 |
| 10 | 14.3 | 32 |
| 30 | 42.9 | 87 |
| 50 | 68.8 | 125 |
| 70 | 93.8 | 154 |
| 90 | 118.8 | 165 |
| 100 | 131.3 | 171 |
| 120 | 157.1 | 182 |
| 150 | 200.0 | 200 |
| 170 | 220.0 | 220 |
| 200 | 250.0 | 250 |
| 300 | 350.0 | 350 |
Adjustment Based On Breakpoints
\[ {\tiny AQI_{U.S.} = 2.54\times 10^{-5} AQI_{China}^3 - 1.31\times 10^{-2} AQI_{China}^2 + 2.59 AQI_{China} } \]
10 Biggest AQI Difference In Photos
Stationary Test
In order to see if the difference in AQI reported by China and U.S. exsits, we check the stationarity of this time series with ADF test.
Stationary Test Result
zeromean <- aqidiff$aqi_diff-mean(aqidiff$aqi_diff)
library(tseries)
pvalue <- adf.test(zeromean)$p.value
pvalue[1] 0.01The test shows the data is stationary. Taking into account of difference average 12.1317722, we can conclude that the difference of AQI reported by China and US really exists.
Seasonal Trend Decomposition
aqidiff.ts<-ts(aqidiff$aqi_diff,frequency=365)
aqidiff.de<-decompose(aqidiff.ts,type="additive")
plot(aqidiff.de)